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Vol. 41, No.3, Summer 2007 177
Systems research has undergone signicant changes in
recent years due to the inclusion of new applications for
control—e.g., microelectronics manufacturing or drug
dosage adjustment for biomedical applications—and the use
of systems concepts in new areas such as systems biology.
As the results from research tend to inuence what is taught
in a classroom and vice versa, it is very important to have
access to illustrative examples that can easily be presented
to undergraduate students without requiring an advanced
background in the systems area.
There are many applications in the eld of drug infusion
control[1-3] that have been developed and used in classroom
example problems. The selection of examples from the eld
of systems biology, however, is much more limited. This is
despite it being widely recognized that feedback loops are
common to many cellular functions.[4-8] This paper addresses
these points as it investigates a signal transduction pathway
involved in the body’s response to inammation or injury,
one of many areas of interest to systems biology. While the
described system is of interest to the biomedical community,
it is simple enough to be presented in an undergraduate class
and contains feedback regulation of the signal transduction
pathway. Additionally, the system can be appropriately de-
scribed using block diagrams and transfer function models
for perturbations around a steady state.
The outline of the paper is as follows: Section 1 is an in-
troduction. Section 2 presents the biological signicance of
A Case Study Representing
SIGNAL TRANSDUCTION IN LIVER CELLS
As a Feedback Control Problem
AbhAy Singh, Arul JAyArAmAn, And Juergen hAhn
Texas A&M University • College Station, TX 77843-3122
ChE classroom
© Copyright ChE Division of ASEE 2007
Abhay Singh is a Ph.D. student at Texas
A&M University, College Station. He re-
ceived his B.E. in chemical engineering
from Panjab University, Chandigarh, India
in 1998. Afterward, he joined Indian Pet-
rochemicals Corporation Ltd. (IPCL) as a
production engineer (Chemical) for four
years. His research interests include sensor
location, soft sensor design, and systems
biology. He is a recipient of the CPC 7 Out-
standing Contributed Paper Award.
Arul Jayaraman received his B.E. (Hons)
in chemical engineering and M.S. (Hons) in
physics from BITS Pilani, India, in 1992, his
M.S. from Tufts University in 1994, and his
Ph.D. from the University of California, Irvine,
in 1998, both in chemical engineering. He
joined Harvard Medical School as instructor
in bioengineering in 2000. He joined Texas
A&M University, College Station, as an assis-
tant professor in 2004. His research interests
include systems biology, molecular bioengi-
neering, and cell-cell communication.
Juergen Hahn received his degree in en-
gineering from RWTH Aachen, Germany,
in 1997, and his M.S. and Ph.D. degrees
in chemical engineering from the University
of Texas, Austin, in 1998 and 2002, respec-
tivel y. He joined Texas A&M Univers ity,
College Station, as an assistant professor
in 2003. His research interests include
process modeling and analysis, systems
biology, and nonlinear model reduction. He
has published more than 30 articles and
book chapters.
Chemical Engineering Education178
the system and describes the model representing the signal
transduction pathway. A block diagram representation of
the signal transduction pathway is developed in Section 3.
Section 4 presents the transfer functions that describe the ef-
fect concentrations of some proteins in the pathway have on
other proteins in the pathway and investigates the dynamic
behavior of the signal transduction pathway. Furthermore,
the dynamics of cells in which the regulatory mechanism
does not function properly, as is often associated with certain
types of cancer,[6] are investigated based upon the developed
transfer function model and compared to the behavior of the
original system. Section 5 presents how this model was used
within an undergraduate process dynamics and control class
taught at Texas A&M University, and Section 6 presents
some conclusions.
TARGET SYSTEM
Cell signaling refers to the process by which cells sense
their environment, including communication with other cells.
Signaling in cells is initiated by extra-cellular molecules that
activate an intracellular signaling pathway, which ultimately
leads to the formation of proteins involved in basic cellular
processes like regulation of cell growth and division or expres-
sion of other, secreted proteins. This entire process
in which biological information is transferred
from extra-cellular signals into changes
inside a cell is referred to as signal
transduction. As malfunction of sig-
naling pathways can be associated
with some diseases, e.g., certain
types of cancer, cells usually have
regulatory mechanisms built into
signal transduction pathways.
The system under investiga-
tion in this paper deals with
signaling pathways involved
in a body’s response to burn-
injury-induced inflammation.
The injured cells release cyto-
kines, one of which is interleukin
6 (IL-6), to the bloodstream. These
cytokines are sensed by hepatocytes
in the liver, and they activate the acute
phase response (APR). The acute phase
response up- or down-regulates the expres-
sion of certain plasma proteins that take part
in the body’s response to the burn-injury-induced
inammation. Investigating cell signaling in hepatocytes
stimulated by inammatory agents is of crucial importance
to understanding the mechanisms underlying the APR.
The specic topic of this paper is the development of a trans-
fer function model of the JAK (Janus-Associated Kinases)/
STAT (Signal Transducers and Activators of Transcription)
signaling pathway in hepatocytes stimulated by IL-6.[9-10] Sig-
naling through the JAK/STAT pathway is regulated by SOCS3
(Suppressors Of Cytokine Signaling 3) proteins. These pro-
teins are induced by the JAK/STAT signaling pathway once
the signal emanating from the cell surface reaches the nucleus
of the cell. SOCS3 regulates further signaling from the cell
surface to the nucleus of the cell by inhibiting the activation
of STAT3, a process that is usually taking place as a result of
binding of IL-6 to the receptors on the cell surface.
BLOCK DIAGRAM REPRESENTATION
The system under investigation is based upon the JAK/
STAT pathway of the model presented in Singh, et al.,[11] and
is shown in Figure 1. The model of the JAK/STAT pathway
consists of 33 ordinary differential equations, in which each
state corresponds to the concentration of a particular protein
or protein complex in either the cytosol or the nucleus. It is as-
sumed that the cytosol is “well-mixed” and, separately, that the
nucleus can also be viewed as “well-mixed.” The differential
equation for a particular component (A) is written as:
dN
dt
A
A produced A consumed
= −
∑ ∑
υ υ
, , ( )1
where vA represents the rate of production/consumption of species
A in a particular reaction. It should be noted that these reac-
tions can also include formation and degradation of
a specic protein/protein complex.
While the availability of the detailed
model can have advantages for ana-
lyzing the dynamic concentration
proles of some specic compo-
nents of the system, e.g., dynam-
ics of phosphorylated STAT3
outside of the nucleus, it is not
always required, nor is it neces-
sarily always feasible, to model
every single component of the
system. Instead, it is important
to know the dynamic proles of
certain key components and the
effect a change in the concentra-
tion of one component has on oth-
ers present in the system. This type
of cause-effect relationship can be
conveniently represented in a block dia-
gram. If the relationships between inputs
and outputs can be appropriately described by
linear ordinary differential equations, then transfer
functions can be derived that capture the input-output behav-
ior of the individual components of the system.
These transfer functions are determined by investigating
individual cause-effect relationships in which step inputs are
Figure 1. (above) JAK/STAT signaling pathway induced
by IL-6 in hepatocytes.
Vol. 41, No.3, Summer 2007 179
used to excite the system. It is then possible to derive the transfer function by numerically determining parameters, such that
the difference between the response of the nonlinear model and the transfer function model is minimized.
The following dynamic relationships were identied as important for describing signaling through the JAK/STAT pathway:
c Effect of IL-6 concentration on the receptor complex concentration
c Effect of changes in the concentration of the receptor complex on concentration of STAT3 in the nucleus
c Effect of concentration of nuclear STAT3 on concentration of formed SOCS3
c Effect of concentration of SOCS3 on the receptor complex concentration that can participate in cell signaling
The last of these four dynamic relationships is responsible for the feedback effect in the pathway. An illustration of the block
diagram can be found in Figure 2.
It should be noted that an increase in IL-6 concentration will lead to an increase in receptor complexes that participate in
signaling, and an increase in the number of receptor complexes will also lead to more signaling and a larger amount of nuclear
STAT3. More nuclear STAT3 will lead to increased transcription and translation of the plasma proteins involved in the APR,
while at the same time it leads to the formation of higher levels of SOCS3. SOCS3, on the other hand, has a negative effect on
the activity in the pathway as it prevents phosphorylation of STAT3 by binding to the receptor complexes.
The concentration of IL-6 is used as the input for the system and the concentration of nuclear STAT3 is used as the output of the model.
SIMULATION STUDIES
In order to identify the transfer functions, the cell is assumed to be at steady state with a constant input of 3.0E-4 nM of IL-6,
resulting in a concentration of the phosphorylated receptor complex (IL6-gp80-gp130-JAK*)2 of 6.973E-4 nM, a concentra-
tion of SOCS3 of 0.1047 nM, and a concentration the nuclear STAT3 dimer (STAT3N*-STAT3N*) of 0.1048 nM. The cell is
perturbed from the steady-state by a step change of ±10% in the concentration of IL-6, which serves as the input to the system.
The obtained output trajectories are used for identication of the following transfer functions:
GIL gP gP JAK
IL s
G
1
2
2
6 80 130
6
5 45
1 65 1
=− − −
( )
−=+
*.
.
== −
− − −
( )
=
STAT N STAT N
IL gP gP JAK
3 3
6 80 130
320
2
* *
*
..
. .
*
92
0 03462 0 4462 1
3
3
2
3
s S
GSOCS
STAT N STAT
+ +
=−33 1 08 1
6 80 130
0 6
4
2
N
e
s
GIL gP gP JAK
s
*
.
*
.
=+
=− − −
( )
−
SSOCS s3
0 0019
1 2 1
=+
.
.
Figure 2. Block diagram representation of signaling pathway implemented in Simulink.
Chemical Engineering Education180
A comparison of the response of the original nonlinear
system and the one obtained from the transfer function model
is shown in Figures 3, 4, and 5. It can be concluded that the
linear transfer function model can adequately represent the
behavior of the original (nonlinear) system. It should be noted
that this rst set of simulation experiments was performed
for the sole reason of determining the quality of the t of the
transfer function models to the response generated by the
nonlinear system. It is also important to keep in mind that
the linear approximation, resulting from the use of transfer
functions, will only be able to represent the original nonlinear
system for excitations near the conditions for which the linear
model was derived.
A second experiment was run using the identied transfer
function model. For these simulations, it was assumed that
the effect of SOCS3 on the phosphorylation of STAT3 had
been removed from the cell, as shown in Figure 6, and in the
block diagram, shown in Figure 7. This effect is similar to a
SOCS3 knockout cell where SOCS3 is not produced, which
has medical signicance associated with certain types of
cancers. The only difference between a SOCS3 knockout cell
and the behavior simulated here is that the feedback part is cut
open after the formation of SOCS3 instead of before.
It can be observed from Figure 8 and Figure 9 that the
signal is not down-regulated due to the absence of the effect
of SOCS3 on the system. The receptor complex (IL6-gp80-
gp130-JAK*)2 (Figure 8) and the nuclear STAT3 dimer
Figure 3. Dynamic response of (IL6-gp80-gp130-JAK*)2
complex for ±10% step change in the IL-6 concentration
around the steady state (0.5 pM IL-6 concentration).
Figure 4. Dynamic response of STAT3N*-STAT3N*
complex for ±10% step change in the IL-6 concentration
Figure 5. Dynamic response of SOCS3 for ±10% step
change in the IL-6 concentration about the steady state
(0.5 pM IL-6 concentration).
Figure 6. JAK/STAT signaling pathway induced by IL-6
in cells where the effect of SOCS3 on phosphorylation of
STAT3 has been removed.
Vol. 41, No.3, Summer 2007 181
m Figure 7. (above) Block diagram of the “open-loop”
signaling pathway implemented in Simulink.
b Figure 8. (left) Dynamic response of (IL6-gp80-gp130-
JAK*)2 complex for ±10% step change in the IL-6 concen-
tration around the steady state (0.5 pM IL-6 concentra-
tion) in SOCS3 knockout cells.
. Figure 9. (below, left) Dynamic response of STAT3N*-
STAT3N* for ±10% step change in the IL-6 concentration
around the steady state (0.5 pM IL-6 concentration) in
SOCS3 knockout cells.
(STAT3N*-STAT3N*) (Figure 9) show a larger deviation
from the steady-state value when compared to the closed-
loop responses shown in Figures 3 and 4. Moreover, the
comparable open-loop response from the nonlinear and the
transfer functions indicate that cell behavior can, locally, be
adequately described by the transfer function model.
MODEL USE IN THE PROCESS DYNAMICS
AND CONTROL COURSE AT TAMU
The presented model has been used at several points
throughout the Process Dynamics and Control course taught
in the chemical engineering department at Texas A&M
University:
1) It is used during the rst week of the semesters when
different systems that include feedback control are
introduced to make the students aware of how often they
come in contact with such systems.
2) The model is revisited when the material about deriv-
ing linear transfer functions from data is covered. In
this specic case the data is generated by the original
Chemical Engineering Education182
nonlinear model whereas the linear transfer functions
represent the model to be t to this data.
3) Since the model contains negative feedback regula-
tion, it is also used when the effect of negative feedback
control on a system is discussed.
Using the same example throughout the semester allows
students to participate in several steps of modeling and model
validation, rather than just performing individual tasks. Also,
this model describing a signal transduction pathway is used
alongside models teaching traditional chemical engineering
processes.
CONCLUSIONS
This paper presented a case study in which a signal transduc-
tion pathway was represented as a block diagram, and linear
transfer function models were identied in individual blocks
for perturbations of the model around a steady state.
The system behavior was broken up into four components,
and each part represented the effect a change in the concen-
tration of one component has on others present in the signal
transduction pathway. This was illustrated in how SOCS3
serves as an inhibitor of the signal transduction pathway,
and how the effect SOCS3 has on the signaling activity can
be appropriately described by negative feedback in the block
diagram representation of the system.
Also shown was how the identied model correctly repre-
sented the behavior of the original system for the three key
components chosen. Simulation studies have been performed
on SOCS3 knockout cells, which can be compared to the
“open-loop” behavior of the system, as there is no effect of
SOCS3 on the signal transduction pathway. It was found that
our identied model appropriately described the behavior of
the SOCS3 knockout cell in this way.
The presented case study can serve as an example for il-
lustrating feedback regulation in cell signaling for process
control education.
ACKNOWLEDGMENT
The authors gratefully acknowledge partial nancial sup-
port from the ACS Petroleum Research Fund (Grant PRF#
43229-G9) and from the National Science Foundation (Grant
CBET# 0706792).
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